Chapter 11: Problem 44
What is the coordination number of each sphere in (a) a simple cubic cell, (b) a body-centered cubic cell, and (c) a face-centered cubic cell? Assume the spheres are all the same.
Short Answer
Step by step solution
Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Simple Cubic Cell
Body-Centered Cubic Cell
In the BCC structure, the central atom directly touches the 8 corner atoms. Also, each corner atom interacts with the center atom and has some associations with neighboring corner atoms as well.
This somewhat tighter packing compared to the simple cubic cell results in better space utilization. Imagine cramming more atoms into the same cube – this is not only a more efficient use of space but also impacts the material's mechanical properties, often making it stronger than materials with a simple cubic structure. Metals such as iron and chromium commonly exhibit a BCC arrangement.
Face-Centered Cubic Cell
The FCC structure, with its high coordination number, is all about maximizing space efficiency. This accounts for why many metals, such as aluminum, copper, and gold, exhibit such a structure – it grants them excellent ductility and malleability. These properties make FCC-structured materials favorable in various applications, like electronics and jewelry. It's fascinating to see how slight changes in atomic arrangement can lead to vastly different physical properties!